Thermal derivation of the Coleman-De Luccia tunneling prescription

Abstract

We derive the rate for transitions between de Sitter vacua by treating the field theory on the static patch as a thermal system. This reproduces the Coleman-De Luccia formalism for calculating the rate, but leads to a modified interpretation of the bounce solution and a different prediction for the evolution of the system after tunneling. The bounce is seen to correspond to a sequence of configurations interpolating between initial and final configurations on either side of the tunneling barrier, all of which are restricted to the static patch. The final configuration, which gives the initial data on the static patch for evolution after tunneling, is obtained from one half of a slice through the center of the bounce, while the other half gives the configuration before tunneling. The formalism makes no statement about the fields beyond the horizon. This approach resolves several puzzling aspects and interpretational issues concerning the Coleman-De Luccia and Hawking-Moss bounces. We work in the limit where the back reaction of matter on metric can be ignored, but argue that the qualitative aspects remain in the more general case. The extension to tunneling between anti-de Sitter vacua is discussed.

Figures (4)

• Figure 1: A potential with two minima.
• Figure 2: A cross-section through the potential energy barrier, illustrating the two modes of escaping from the false vacuum: thermal excitation to A, followed by tunneling to B; and thermal excitation to the top of the barrier.
• Figure 3: The two types of bounces at finite temperature for flat spacetime. The shaded areas denote regions where the field is on the true vacuum side of the barrier. In both cases the imaginary time $\tau$ runs vertically, while the horizontal direction represents the three spatial directions. In each diagram the top and bottom solid lines are identified, making $\tau$ compact. The bounce in (a) corresponds to thermally assisted tunneling from the approximately false vacuum configuration on the $\tau$ slice represented by the solid lines to the configuration on the $\tau$ slice indicated by the dashed line. These two configurations are connected by a series of intermediate configurations, corresponding to the dotted lines. The $\tau$-independent bounce in (b) corresponds to thermal excitation over the barrier. A constant-$\tau$ slice through this bounce gives a critical bubble configuration, which is a saddle point on the potential energy barrier.
• Figure 4: Slices of constant $\tau$ projected onto the $y^4$-$y^5$ plane. The correspondence with those in the flat-spacetime bounce of Fig. \ref{['hiTphi']}a is indicated by the form of the lines. The initial and final configurations of the tunneling path correspond to the solid and dashed lines, respectively, while intermediate configurations are obtained from slices along the dotted lines.